I went to Israel a few years ago and you'll find that the hotels are mostly well equipped. You can often get away these days with just packing a USB charger and plugging it into the TV in the room to charge your phone. If you have some cash spare, it's worth purchasing an adapter that takes USB and has all of the plugs - if you're not travelling with a laptop (where you'll need a full adapter) that's your best bet. Something like this.
You will likely get screened with your luggage (checked/carry on alike - I had to unpack and repack my bag for security) in Tel Aviv - the security process there is very thorough. I honestly don't think it will make much difference if you have checked or carry-on only. This is both exiting and entering the country. Make sure you allow plenty of time at the airport as it's not so much the bag screening, but the immigration process that takes a long time (be ready for lots of questions).
Finally, have a great time! I loved Jerusalem - a fascinating historical city. Tel Aviv is a very modern city full of life with fantastic food. Also, one place I would absolutely not miss (and is probably one of the most amazing places I have ever been) is Wadi Rum in Jordan. I'm posting photo because it's too hard to describe how amazing it was!